Approximate Separability of the Green's Function of the Helmholtz Equation in the High Frequency Limit

摘要

The minimum number of terms that are needed in a separable approximation for a Green's function reveals the intrinsic complexity of the solution space of the underlying differential equation. It also has implications for whether low-rank structures exist in the linear system after numerical discretization. The Green's function for a coercive elliptic differential operator in divergence form was shown to be highly separable [2], and efficient numerical algorithms exploiting low-rank structures of the discretized systems were developed.